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|a 10.1007/978-3-0348-8687-1
|2 doi
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|a (OCoLC)812613119
|z (OCoLC)812165098
|z (OCoLC)952183539
|z (OCoLC)1001511505
|z (OCoLC)1113450596
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|a Flucher, Martin,
|d 1962-
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|a Variational problems with concentration /
|c Martin Flucher
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| 260 |
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|a Basel ;
|a Boston :
|b Birkhauser,
|c ©1999
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| 300 |
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|a 1 online resource (viii, 163 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
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|a text file
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|b PDF
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|a Progress in nonlinear differential equations and their applications ;
|v v. 36
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|a Includes bibliographical references (pages 151-160) and index
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|a 1 Introduction -- 2 P-Capacity -- 3 Generalized Sobolev Inequality -- 3.1 Local generalized Sobolev inequality -- 3.2 Critical power integrand -- 3.3 Volume integrand -- 3.4 Plasma integrand -- 4 Concentration Compactness Alternatives -- 4.1 CCA for critical power integrand -- 4.2 Generalized CCA -- 4.3 CCA for low energy extremals -- 5 Compactness Criteria -- 5.1 Anisotropic Dirichlet energy -- 5.2 Conformai metrics -- 6 Entire Extremals -- 6.1 Radial symmetry of entire extremals -- 6.2 Euler Lagrange equation (independent variable) -- 6.3 Second order decay estimate for entire extremals -- 7 Concentration and Limit Shape of Low Energy Extremals -- 7.1 Concentration of low energy extremals -- 7.2 Limit shape of low energy extremals -- 7.3 Exploiting the Euler Lagrange equation -- 8 Robin Functions -- 8.1 P-Robin function -- 8.2 Robin function for the Laplacian -- 8.3 Conformai radius and Liouville's equation -- 8.4 Computation of Robin function -- 8.5 Other Robin functions -- 9 P-Capacity of Small Sets -- 10 P-Harmonic Transplantation -- 11 Concentration Points, Subconformai Case -- 11.1 Lower bound -- 11.2 Identification of concentration points -- 12 Conformai Low Energy Limits -- 12.1 Concentration limit -- 12.2 Conformai CCA -- 12.3 Trudinger-Moser inequality -- 12.4 Concentration of low energy extremals -- 13 Applications -- 13.1 Optimal location of a small spherical conductor -- 13.2 Restpoints on an elastic membrane -- 13.3 Restpoints on an elastic plate -- 13.4 Location of concentration points -- 14 Bernoulli's Free-boundary Problem -- 14.1 Variational methods -- 14.2 Elliptic and hyperbolic solutions -- 14.3 Implicit Neumann scheme -- 14.4 Optimal shape of a small conductor -- 15 Vortex Motion -- 15.1 Planar hydrodynamics -- 15.2 Hydrodynamic Green's and Robin function -- 15.3 Point vortex model -- 15.4 Core energy method -- 15.5 Motion of isolated point vortices -- 15.6 Motion of vortex clusters -- 15.7 Stability of vortex pairs -- 15.8 Numerical approximation of vortex motion
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|a The subject of this research monograph is semilinear Dirichlet problems and similar equations involving the p-Laplacian. Solutions are constructed by a constraint variational method. The major new contribution is a detailed analysis of low-energy solutions. In PDE terms the low-energy limit corresponds to the well-known vanishing viscosity limit. First it is shown that in the low-energy limit the Dirichlet energy concentrates at a single point in the domain. This behaviour is typical of a large class of nonlinearities known as zero mass case. Moreover, the concentration point can be identified in geometrical terms. This fact is essential for flux minimization problems. Finally, the asymptotic behaviour of low-energy solutions in the vicinity of the concentration point is analyzed on a microscopic scale. The sound analysis of the zero mass case is novel and complementary to the majority of research articles dealing with the positive mass case. It illustrates the power of a purely variational approach where PDE methods run into technical difficulties. To the readers benefit, the presentation is self-contained and new techniques are explained in detail. Bernoullis free-boundary problem and the plasma problem are the principal applications to which the theory is applied. The author derives several numerical methods approximating the concentration point and the free boundary. These methods have been implemented and tested by a co-worker. The corresponding plots are highlights of this book
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|a Electronic reproduction
|b [Place of publication not identified] :
|c HathiTrust Digital Library,
|d 2012.
|5 MiAaHDL
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|a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
|u http://purl.oclc.org/DLF/benchrepro0212
|5 MiAaHDL
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|a English
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|a Print version record
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|a Boundary value problems
|x Numerical solutions
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|a Differential equations, Elliptic
|x Numerical solutions
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|a Variational principles
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|a Boundary value problems
|x Numerical solutions
|2 fast
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|a Differential equations, Elliptic
|x Numerical solutions
|2 fast
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|a Elliptisches System
|x Freies Randwertproblem
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|a Elliptisches System
|x Variationsproblem
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|a Freies Randwertproblem
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|a Variational principles
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|a Variationsproblem
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|a Variationsproblem
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|i Print version:
|a Flucher, Martin, 1962-
|t Variational problems with concentration
|d Basel ; Boston : Birkhauser, ©1999
|w (DLC) 99038073
|w (OCoLC)41674411
|
| 830 |
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|a Progress in nonlinear differential equations and their applications ;
|v v. 36
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